The nonclassical diffusion equations with time-dependent memory kernels and a new class of nonlinearities

Thuy, Le Thi and Toan, Nguyen Duong (2022) The nonclassical diffusion equations with time-dependent memory kernels and a new class of nonlinearities. Glasgow Mathematical Journal, 64 (3). pp. 716-733. ISSN 1469509X

Abstract

In this study, we consider the nonclassical diffusion equations with time-dependent memory kernels Formula Presentedon a bounded domain Formula Presented. Firstly, we study the existence and uniqueness of weak solutions and then, we investigate the existence of the time-dependent global attractors Formula Presented in Formula Presented. Finally, we prove that the asymptotic dynamics of our problem, when Formula Presented approaches a multiple Formula Presented of the Dirac mass at zero as Formula Presented, is close to the one of its formal limit Formula PresentedThe main novelty of our results is that no restriction on the upper growth of the nonlinearity is imposed and the memory kernel Formula Presented depends on time, which allows for instance to describe the dynamics of aging materials.

Item Type:	Article
Identification Number:	10.1017/S0017089522000027
Depositing User:	maria
Date Deposited:	10 Jun 2024 03:08
Last Modified:	10 Jun 2024 03:08
URI:	http://repository.ub.ac.id/id/eprint/220673

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